Related papers: Generating random bigraphs with preferential attac…
We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a…
This paper analyzes key properties of networks generated by geometric preferential attachment. We establish that the expected number of triangles is proportional to that of the standard preferential attachment model, with a proportionality…
Real-world networks tend to be scale free, having heavy-tailed degree distributions with more hubs than predicted by classical random graph generation methods. Preferential attachment and growth are the most commonly accepted mechanisms…
We propose a new approach to text semantic analysis and general corpus analysis using, as termed in this article, a "bi-gram graph" representation of a corpus. The different attributes derived from graph theory are measured and analyzed as…
Community detection in graphs, data clustering, and local pattern mining are three mature fields of data mining and machine learning. In recent years, attributed subgraph mining is emerging as a new powerful data mining task in the…
We study a random graph $G_n$, which combines aspects of geometric random graphs and preferential attachment. The resulting random graphs have power-law degree sequences with finite mean and possibly infinite variance. In particular, the…
We consider preferential attachment random graphs which may be obtained as follows: It starts with a single node. If a new node appears, it is linked by an edge to one or more existing node(s) with a probability proportional to function of…
We develop a new framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world…
Inferring missing links or detecting spurious ones based on observed graphs, known as link prediction, is a long-standing challenge in graph data analysis. With the recent advances in deep learning, graph neural networks have been used for…
In real life, networks are dynamic in nature; they grow over time and often exhibit power-law degree sequences. To model the evolving structure of the internet, Barab\'{a}si and Albert introduced a simple dynamic model with a power-law…
It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…
The S-metric has grown popular in network studies, as a measure of ``scale-freeness'' restricted to the collection G(D) of connected graphs with a common degree sequence D=(d_1,\ldots,d_n). The calculation of S depends on the maximum…
Bipartite graphs have received some attention in the study of social networks and of biological mutualistic systems. A generalization of a previous model is presented, that evolves the topology of the graph in order to optimally account for…
We introduce a new type of preferential attachment tree that includes choices in its evolution, like with Achlioptas processes. At each step in the growth of the graph, a new vertex is introduced. Two possible neighbor vertices are selected…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Random hypergraph is a broad concept used to describe probability distributions over hypergraphs, which are mathematical structures with applications in various fields, e.g., complex systems in physics, computer science, social sciences,…
In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…
Because of the huge number of graphs possible even with a small number of nodes, inference on network structure is known to be a challenging problem. Generating large random directed graphs with prescribed probabilities of occurrences of…
A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that the problem of generating planar tanglegrams uniformly at…
In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most graph generating…